Posers and Puzzles

Posers and Puzzles

  1. Joined
    09 Aug '06
    Moves
    5363
    07 Jun '08 11:37
    Mr. Jones went to a bank to cash a check. The teller switched the dollars and cents. Mr. Jones was given dollars instead of cents and cents instead of dollars. After buying a five-cents newspaper, Jones discovered that he had exactly twice as much as his original check. What was the amount of the check?
  2. Joined
    12 Sep '07
    Moves
    2668
    07 Jun '08 11:553 edits
    Suppose his check was worth $d and c cents, or 100d+c (d,c < 100).He was given 100c+d, and after the newspaper had (100c+d-5)=2(100d+c)
    100c+d-5=200d+2c
    98c=199d+5
    0=3d+5 (98)
    93=3d (98)
    We can't divide through mods but we can multiply by 33 (same result anyways)
    31=d (98)
    As 0
  3. Joined
    12 Sep '07
    Moves
    2668
    07 Jun '08 11:563 edits
    Suppose his check was worth $d and c cents, or 100d+c (d,c < 100).He was given 100c+d, and after the newspaper had (100c+d-5)=2(100d+c)
    100c+d-5=200d+2c
    98c=199d+5
    0=3d+5 (98)
    93=3d (98)
    We can't divide through mods but we can multiply by 33 (same result anyways)
    31=d (98)
    As 0 is less than d is less than100, d=31 and it follows that c=63
    The check was worth $31.63

    Sorry about the double post, for some reason all the text after i typed the 'less than to' sign was cut off. I dunno why that didn't happen with my first one though. Wierd.
  4. Standard memberthyme
    Undutchable
    was here
    Joined
    23 Jul '07
    Moves
    83545
    08 Jun '08 08:17
    you need two independent equations.

    The original check was for the amount of 100d + c cents
    he got 100c + d cente

    100d + c - 5 = 200d + 2 c ... first equation


    The second equation: we know c has to be bigger than d. c should either be twice d or c = 2d+1

    solve:
    1. 100d + c - 5 = 200d + 2c
    2. c = 2d+1

    Answer: 31 dollars 63 cents
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